I'm not sure where you get the number 64 there. And indeed, the optimization toolbox will not help you, at least not directly.
You tell us you have 25 input parameters, with 4 levels for each parameter to tune. So we would see
4^25 = 2^50 = 1.12589990684262e+15
distinct combinations of parameters. 64 would never enter into the question.
Regardless, this is a nonlinear integer programming problem, but the optimization toolbox does not provide such a tool. That is, you have 25 variables, each of which can effectively take on the values 1, 2, 3 or 4. Thus effectively an integer problem. It is nonlinear because the output is related in a general black box, nonlinear way to those inputs.
Thus intlinprog from the optimization toolbox solve LINEAR integer programming problems, but not nonlinear ones. And fmincon or fminunc (etc.) can solve general problems, but are not able to handle integer constraints on the parameters. So nothing in the standard optimization toolbox can help you out.
You will need to look in the global optimization toolbox to find a solver that can handle your problem. A quick check shows that ga can minimize a nonlinear function, AND admit integer constraints on the variables. In fact, a quick check shows that ONLY ga solves that class of problem. So you must use ga. If you don't have the global optimization toolbox, then you will need to get it.
If that is completely not an option, I do recall a tool called fminconset on the file exchange that will solve this class of problem, so you could try using this:
However, I would note that it was last updated in the year 2000, so it is effectively 18 years out of date. It might not run by now. Since it uses fmincon itself, the odds are good that something has changed with fmincon since to prevent it from running properly. You never know with a tool that old.